Question: $(-19+7i)-(29+32i)=$ Express your answer in the form $(a+bi)$.
Solution: Background Complex numbers can be added or subtracted by separately adding or subtracting their real and imaginary terms. To add or subtract complex numbers: Expand parentheses (attending to minus signs outside of parentheses if necessary) Combine all real terms (terms that do not contain $i$ ), and add or subtract them. Combine all imaginary terms (terms that contain $i$ ), and add or subtract them. Combining Like Terms $\begin{aligned} ({-19}+{7}i)-({29}+{32}i)&={-19}+{7}i-{29}-{32}i \\\\ &={-19}-{29}+{7}i-{32}i \\\\ &={-48}{-25}i \end{aligned}$ Summary $({-19}+{7}i)-({29}+{32}i)={-48}{-25}i$